Damn hot..?
How hot is it..!?
If below 50°C..I still consider it only warm and nothing to be worried about. So far my phone reach less than 45°C even when I do surfing.

The s4 has a lot of stuff running in background also. Nfc. That eye scanning thingy. Smart stay. Whatever stuff. If u dun use I recommend switching off. Also as usual make sure u close unused apps properly. And off gps if not using too.

Take a look at "BetterBatteryStats" - https://play.google.com/store/apps/details?...terbatterystats

For underclocking and undervolting recommend setcpu. On playstore. However the ability to do noth would depend on whether u are rooted and whether your kernel supports it. If it does u will wanna tread carefully as it can cause your device to crash and the only way to fix would be a factory reset. Uncle benny can shed more light on how much u can reduce the voltage to a minimum of 800mv. I generally reduce all by 75mv for my note 2 to a minimum of 800mv (or if by default already lower I dont touch)